24 January 2008

A list of logical fallacies

Most of these are extra-mathematical fallacies. For example, in mathematics we don't often see a relation "X causes Y", although it is quite common in ordinary discourse. Even in probability and statistics, we don't see causation nearly as often as correlation. However, they may be familiar to mathematicians as "false methods of proof". For example, what this list calls appeal to force is the well-known "proof by intimidation" -- the Important Person at the front of the room says it's true, so it must be!

A lot of these fallacies are essentially statistical in nature, as any reasoning about the real world must be. In mathematics we either know things or we do not; we don't attach probabilities to our knowledge. (However, we can attach probabilities to other people's knowledge -- or to our own extra-mathematical knowledge -- and then reason about those probabilities. This is the basis of Bayesian reasoning.) Many others are fallacies that exploit the ambiguitiy of natural language. Perhaps the power of mathematics is that it allows us to know things surely, which can never happen in the Real World. But on the flip side, mathematicians know fewer things than other people, because we insist on such certainty in our knowledge.